Singapore-based practical guides, tutorials and experiments in AI, computing, modelling, simulation, optimisation and quantum computing, with research notes and hands-on workflows.

Quantum Computing: A Complete Learning Path

A guided index to the Quantum Series: thirteen hands-on posts ordered as a learning path, from qubits and the Bloch sphere to Grover’s algorithm.

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QUANTUM SERIES 2026
The complete learning path, from a single qubit to Grover’s algorithm.

This is the index to the Techucation Quantum Series: a sequence of hands-on posts that build quantum computing from the ground up. Each one stands on its own, but together they form a single arc, from what a qubit actually is, through the rules that make quantum mechanics strange, to the algorithms that turn those rules into a real speedup. The order below is a learning path from first principles to algorithms, not the order the posts were written.

New to the topic? Read top to bottom. Already comfortable with qubits and gates? Skip ahead to the algorithms in Section 4. Explore all related research in the Quantum Computing Hub.

Foundational Pre-reading: The Math Behind the Phase

0

Euler’s Formula: Why eiφ Is Just Shorthand for a Circle

Optional warm-up before the qubit posts: the complex plane, i as a 90° rotation, and why the phase factor eiφ traces a circle.

1  ·  Start Here: Qubits, Superposition & Two-Qubit Entanglement

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Quantum Computing From First Principles: Qubits, Hadamard Gates & Why H² = I

First principles: what a qubit is, how the Hadamard gate builds superposition, and why tensor products scale the state space.

2

Bloch Sphere Explained: Basis States and the X and Z Gates

The geometric bridge from qubit statevectors to gates: where |0⟨, |1⟨, |+⟨ and |−⟨ sit, how X and Z rotate them, and how to verify the result in Qiskit.

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Hands-on Lab: Drawing Quantum Diagrams with Matplotlib on Termux

A tested workflow for rendering high-resolution Bloch spheres and circuit diagrams directly in Android Termux when full Qiskit will not complete.

3

Two-Qubit Entanglement Explained: The 4 Bell States, Mathematical Non-Separability, and Qiskit Implementation

Moving beyond single qubits: tensor products, product states vs entangled states, Schmidt decomposition, CNOT as the universal entanglement generator, the four Bell states, Bell basis decoding, and why the single-qubit Bloch vector collapses.

2  ·  The Hadamard Toolkit

4

The Quantum Fourier Transform of a Single Qubit is the Hadamard Transform

The one-qubit QFT turns out to be exactly the Hadamard gate, a small result that anchors the bigger picture.

5

The Walsh-Hadamard Matrix: Backbone of Grover’s Diffusion Operator

How the Hadamard sign table generalises to n qubits and powers Grover’s diffusion step.

3  ·  The Rules of the Quantum World

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Reversible Computation in Quantum Computing

Why every quantum gate must be reversible, and how ancilla bits turn irreversible logic into unitary logic.

7

The Cost of Garbage in Quantum Computing

Leftover junk qubits destroy interference; uncomputation cleans them up to protect the speedup.

8

The No-Cloning Theorem: Why You Cannot Copy a Qubit

A short proof that an unknown quantum state cannot be duplicated, and what that impossibility makes possible.

9

Quantum Teleportation, and Why It Is Not Cloning

Moving an unknown qubit from one place to another without ever copying it, using entanglement and two classical bits.

4  ·  Algorithms

10

Understanding Phase Kickback

The mechanism where the target qubit flips the control’s phase, the trick underneath Deutsch’s, Grover’s, and Shor’s.

11

Deutsch’s Algorithm: The Four Cases

The four one-bit Boolean functions, the reversible oracle, and the single query that beats the classical two.

12

Deutsch Revisited: Quantum vs Classical in Qiskit

The same algorithm in running Qiskit code: two classical queries against one quantum query.

13

The Deutsch-Jozsa Algorithm: Exponential Speedup & 4 Canonical Oracles

Scaling to n-qubit Boolean functions: provable exponential query separation, phase kickback, the four canonical oracles, and Qiskit 2.x implementation.

14

Grover’s Algorithm: Inversion About the Mean

A full three-qubit walkthrough of the oracle and the amplitude amplification that surfaces the marked item.

5  ·  Entanglement in Action: Bell’s Inequality

15

The CHSH Game Simulator and Bell’s Inequality

Putting entanglement into action: an interactive simulator where quantum correlation violates Bell’s inequality, beats the classical 75 percent ceiling, and reaches the Tsirelson bound (85.4%).


Quantum Series 2026  ·  Built with Qiskit 1.x

✦ This article was generated with the assistance of Claude by Anthropic ✦

Continue the Quantum Series
← The CHSH Game Simulator & Bell’s Inequality (Module 15)
View the complete Quantum Computing learning path
→ Start with qubits and Hadamard gates (Module 1)
• Browse all articles in the Quantum Computing Hub →